Question

which transformation would take figure a to figure b? answer a clockwise rotation of 180° about the origin a reflection over the line y = x a reflection over the line y = -x a clockwise rotation of 90° about the origin

Explanation:

Step1: Recall rotation rules

For a 180 - degree clock - wise rotation about the origin, the transformation rule for a point $(x,y)$ is $(x,y)\to(-x,-y)$. For a 90 - degree clock - wise rotation about the origin, the rule is $(x,y)\to(y, - x)$. For reflection over $y = x$, the rule is $(x,y)\to(y,x)$ and for reflection over $y=-x$, the rule is $(x,y)\to(-y,-x)$.

Step2: Analyze the orientation and position of figures

Figure A and Figure B have a 90 - degree clock - wise rotation relationship about the origin. If we take a point on Figure A, say $(-8,-1)$ and apply a 90 - degree clock - wise rotation about the origin $(x,y)\to(y, - x)$, we get $(-1,8)$ which is consistent with the position of the corresponding point on Figure B.

Answer:

A clockwise rotation of 90° about the origin